AP Precalculus 1.1-1.3

Front

What is the average rate of change of a function on an interval [a, b]?

Back

The average rate of change of a function f(x) on the interval [a, b] is given by the formula: (f(b) - f(a)) / (b - a).

Front

Define 'average rate of change'.

Back

The average rate of change of a function over an interval is the change in the function's value divided by the change in the input value over that interval.

Front

What does it mean for the average rate of change to be decreasing?

Back

It means that as the input values increase, the output values are increasing at a slower rate, indicating a concave down behavior of the function.

Front

How do you determine the average rate of change on the interval (0, 3) if f(0) = 2 and f(3) = 5?

Back

Average rate of change = (f(3) - f(0)) / (3 - 0) = (5 - 2) / 3 = 1.

Front

What is the significance of the interval (-∞, 1) in relation to average rate of change?

Back

It indicates the range of x-values over which the average rate of change is being analyzed, often to find where it is decreasing.

Front

Explain the concept of a function's graph representing motion.

Back

A function's graph can represent motion by showing the relationship between time (x-axis) and position (y-axis), illustrating how position changes over time.

Front

What is the formula for calculating the average rate of change between two points?

Back

The formula is: Average Rate of Change = (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are two points on the graph.

Front

What does it mean if a function has a constant average rate of change?

Back

It means the function is linear, and the slope of the line connecting any two points on the graph is the same.

Front

How can you visually identify the average rate of change on a graph?

Back

You can draw a secant line between two points on the graph; the slope of this line represents the average rate of change.

Front

What is the average rate of change of the function f(x) = 2x + 3 on the interval [1, 4]?

Back

Average rate of change = (f(4) - f(1)) / (4 - 1) = (11 - 5) / 3 = 2.